[tex]x - bile \: albe \\ y - bile \: rosii \\ z - bile \: albastre [/tex]
[tex]P = \frac{nr. \: cazuri \: favorabile}{nr. \: cazuri \: posibile} [/tex]
[tex]nr. \: cazuri \: posibile = nr. \: total \: de \: bile = 48[/tex]
[tex]P_{x} = \frac{1}{3} [/tex]
[tex]P_{x} = \frac{x}{48} [/tex]
[tex] = > \frac{x}{48} = \frac{1}{3} = > x = \frac{48 \times 1}{3} = \frac{48}{3} = 16[/tex]
[tex]P_{z} = \frac{5}{12} [/tex]
[tex]P_{z} = \frac{z}{48} [/tex]
[tex] = > \frac{z}{48} = \frac{5}{12} = > z = \frac{48 \times 5}{12} = 4 \times 5 = 20[/tex]
[tex]x + y + z = 48[/tex]
[tex]16 + y + 20 = 48[/tex]
[tex]y = 48 - 16 - 20[/tex]
[tex]y = 12[/tex]
